Data acquisition and analysis is an important part of many test and evaluation plans for proving component health under real-word situations and further improving component longevity. Launch Vehicles, such as rockets, experience vibration of varying frequencies and amplitudes due in part to engine combustion, liftoff acoustics, aerodynamic effects, and pyrotechnic events. Thus, there is an ongoing need to measure vibrations during flight, transmit vibration measurements to a ground station, and characterize and understand the vibrations to develop test requirements for components, such as avionics, propulsion, ordnance, etc. Similarly, there is an ongoing need to measure vibrations during ground test where the vibration in flight is replicated on an electro dynamic shaker. Moreover, there is a need to monitor vehicle health in order to rapidly diagnose anomalies should such anomalies appear.
When acquiring samples, or measurements, that vary over time in order to characterize the vibration that may be affecting a launch vehicle, such samples may be acquired from one or more accelerometers or displacement sensors that measure motion. Such time domain measurements may then be transformed into the frequency domain for analysis. Aliasing of one or more frequencies present in the vibration, or acceleration, poses a risk of corrupting data such that high frequency vibrations may appear as low frequency vibrations, for example. As illustrated in FIG. 1A, one or more samples 108 of the time varying signal 104 may be acquired. As one example, the time varying signal 104 may be indicative of a vibration occurring at a launch vehicle during flight. Although one or more samples 108 of the time varying signal 104 may be acquired, the frequency, or rate, at which the samples are acquired may play a role in corrupting such measurements when the one or more samples 108 of the time varying signal 104 are used to reconstruct and/or characterize the time varying signal 104. Thus, improperly acquired samples 108 of the time varying signal 104 may lead to aliasing such that a signal 112 having a frequency different from the frequency of the time varying signal 104 is reconstructed.
Current vibration measurement solutions utilize uniform sampling, as depicted in FIG. 1B, to acquire measurement samples 116 at a uniform sample rate with a constant time between samples and in order to collect valid data up to a frequency dependent on the defined sample rate. Further, a frequency, or rate, at which the uniformly spaced samples are acquired may account for the effects of aliasing of a signal having a particular known frequency of interest. That is, generally accepted sampling theory states that to collect valid data up to a defined frequency, the data (if uniformly sampled) must be sampled at a rate at least twice that of the defined frequency. This required sample rate is known as “the Nyquist rate.” As an example, to measure a vibration occurring at 2,000 Hz (that is 2,000 vibrations per second), the vibration must be sampled at a rate that is faster than 4,000 samples per second. However, high frequency vibration cycles occurring above 2,000 Hz may be acquired in such measurements and may lead to data corruption and/or an improper data interpretation. For example, FIG. 2 depicts a representation of a signal 204 in the time domain and in the frequency domain. The signal 204 includes content at various frequencies below 1,000 Hz as well as content at various frequencies above 1,000 Hz. When sampled, content occurring at a frequency above the Nyquist rate, such as frequencies 212A and 212B, may fold over and appear as if such content exists in the frequency band from 0 Hz to the frequency of the Nyquist rate, as depicted by the peaks 216A and 216B. In other words, content occurring at a frequency above the Nyquist rate may corrupt the signal content when such content is reconstructed.
Although anti-aliasing filters may be utilized to reduce a likelihood of aliased content, signals having frequency content in the vicinity of an upper frequency of the antialiasing filter or higher frequency with significantly larger amplitude than in the frequency range of interest may still have a high potential of aliasing, as depicted in FIGS. 3A and 3B.